Mathematical model for dynamic hysteresis loops

Chua, Leon O.; Stromsmoe, K.A.

doi:10.1016/0020-7225(71)90046-2

Cited by 57 publications

(17 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The work of Hodgdon [11] and Coleman and Hodgdon [4] shows that Bouc's model is useful in applied electromagnetics because the functions and parameters can be fine tuned to match experimental results in a given situation. Chua and Stromsoe [2] and Chua and Bass [3] presented also another general theory of hysteresis, considering constitutive models that take the form of first-order differential equations. The main advantages of their models over existing models is its simplicity and the constructive procedure available for determining the nonlinear functions describing the model.…”

Section: Introductionmentioning

confidence: 99%

A new dynamic model of hysteresis in harmonic drives

Dhaouadi

Ghorbel

Gandhi

2003

IEEE Trans. Ind. Electron.

106

View full text Add to dashboard Cite

In this paper, we propose a new dynamic model to describe the hysteresis phenomenon in harmonic drives. The experimental observation of the dynamic torque-displacement relationship for a harmonic drive shows a hysteresis characteristic indicating the simultaneous presence of energy storage and energy dissipation mechanisms. To completely characterize these mechanisms and yet have a simple representation for control, we develop a new hysteresis model using the heredity concept of dynamic systems. This model represents the hysteresis phenomenon by a combination of a nonlinear stiffness component and a nonlinear damping component leading to a mathematically well-posed nonlinear differential equation. The parameters of the model are identified using optimization techniques. We present some important mathematical properties of the model that give insight into model behavior and thus establish a mathematical basis for control. Numerical simulations in comparison with experimental data using our Harmonic Drive Test Apparatus verify the accuracy of the proposed model to represent the complex hysteresis dynamics of harmonic drives.

show abstract

Section: Introductionmentioning

confidence: 99%

A new dynamic model of hysteresis in harmonic drives

Dhaouadi

Ghorbel

Gandhi

2003

IEEE Trans. Ind. Electron.

106

View full text Add to dashboard Cite

show abstract

“…In modeling the hysteretic processes, one of the widely known models to describe the behavior of ferromagnetic materials was suggested by Preisach, as geometric interpretation of the model proposed by Weiss and Freudenreich [31]. The other well-known models of hysteresis were studied by Duhem [31], Ishlinskii [31], Chua and Stromsmoe [32], and Jiles and Atherton [33]. The reader can refer to the work of Mayergoyz for other mathematical models for hysteresis [34].…”

Section: Bouc-wen Model Of Hysteresismentioning

confidence: 99%

A Hysteresis-Based Steering Feel Model for Steer-by-Wire Systems

Arslan

2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

A mathematical model of steering feel based on a hysteresis model is proposed for Steer-by-Wire systems. The normalized BoucWen hysteresis model is used to describe the steering wheel torque feedback to the driver. By modifying the mathematical model of the hysteresis model for a steering system and adding custom parameters, the availability of adjusting the shape of steering feel model for various physical and dynamic conditions increases. Addition of a term about the tire dynamics to the steering feel model renders the steering wheel torque feedback more informative about the tire road interaction. Some simulation results are presented to establish the feasibility of the proposed model. The results of hardware-in-the-loop simulations show that the model provides a realistic and informative steering feel.

show abstract

“…The objective of this study is to contribute towards stability analysis of systems with linear forward dynamics (of an arbitrary order) and static hysteresis nonlinearity in the feedback channel. While the dynamic hysteresis loops have also been described and analyzed, e.g., in [8], the rate-independent hysteresis nonlinearity will be our main focus, for details see [9]. It is worth noting that this type of hysteresis, where rate-independent maps have a persistent memory of the past after the transients have died out, is particularly relevant for multiple natural and artificial systems, in other words engineering systems.…”

Section: Introductionmentioning

confidence: 99%

On stability of linear dynamic systems with hysteresis feedback

Ruderman

2020

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

The stability of linear dynamic systems with hysteresis in feedback is considered. While the absolute stability for memoryless nonlinearities (known as Lure's problem) can be proved by the well-known circle criterion, the multivalued rate-independent hysteresis poses significant challenges for feedback systems, especially for proof of convergence to an equilibrium state correspondingly set. The dissipative behavior of clockwise input-output hysteresis is considered with two boundary cases of energy losses at reversal cycles. For upper boundary cases of maximal (parallelogram shape) hysteresis loop, an equivalent transformation of the closed-loop system is provided. This allows for the application of the circle criterion of absolute stability. Invariant sets as a consequence of hysteresis are discussed.Several numerical examples are demonstrated, including a feedback-controlled double-mass harmonic oscillator with hysteresis and one stable and one unstable poles configuration.

show abstract

Mathematical model for dynamic hysteresis loops

Cited by 57 publications

References 5 publications

A new dynamic model of hysteresis in harmonic drives

A new dynamic model of hysteresis in harmonic drives

A Hysteresis-Based Steering Feel Model for Steer-by-Wire Systems

On stability of linear dynamic systems with hysteresis feedback

Contact Info

Product

Resources

About